Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?

let's $$l_s$$ is length of slower train and $$l_f$$ is length of faster train.
So according to second condition when two trains are moving in same direction
$$l_s = v_{fs} \times t$$  (where $$v_{fs}$$ is relative velocity of faster train w.r.t. slower train and t is time taken to cross it)
or $$l_s = \frac{(60-50) \times 5}{18} \times 18$$ = 50 meter
Only option which has length of slower train as 50 is C.